/**
 * A 4x4 Matrix.
 *
 * @example
 * // Simple rig for rotating around 3 axes
 * let m = new THREE.Matrix4();
 * let m1 = new THREE.Matrix4();
 * let m2 = new THREE.Matrix4();
 * let m3 = new THREE.Matrix4();
 * let alpha = 0;
 * let beta = Math.PI;
 * let gamma = Math.PI/2;
 * m1.makeRotationX( alpha );
 * m2.makeRotationY( beta );
 * m3.makeRotationZ( gamma );
 * m.multiplyMatrices( m1, m2 );
 * m.multiply( m3 );
 */
import {Vector3} from "./Vector3";
import {IVector3} from "./types";

export class Matrix4 {

    readonly isMatrix4 = true;
    isMatrix3?: false;

    constructor() {

        this.elements = [

            1, 0, 0, 0,
            0, 1, 0, 0,
            0, 0, 1, 0,
            0, 0, 0, 1

        ];

        if ( arguments.length > 0 ) {

            console.error( 'THREE.Matrix4: the constructor no longer reads arguments. use .set() instead.' );

        }

    }

    /**
     * Array with matrix values.
     */
    elements: number[];

    /**
     * Sets all fields of this matrix.
     */
    set(
        n11: number,
        n12: number,
        n13: number,
        n14: number,
        n21: number,
        n22: number,
        n23: number,
        n24: number,
        n31: number,
        n32: number,
        n33: number,
        n34: number,
        n41: number,
        n42: number,
        n43: number,
        n44: number
    ): this {

        let te = this.elements;

        te[ 0 ] = n11; te[ 4 ] = n12; te[ 8 ] = n13; te[ 12 ] = n14;
        te[ 1 ] = n21; te[ 5 ] = n22; te[ 9 ] = n23; te[ 13 ] = n24;
        te[ 2 ] = n31; te[ 6 ] = n32; te[ 10 ] = n33; te[ 14 ] = n34;
        te[ 3 ] = n41; te[ 7 ] = n42; te[ 11 ] = n43; te[ 15 ] = n44;

        return this;

    }

    /**
     * Resets this matrix to identity.
     */
    identity(): this {

        this.set(

            1, 0, 0, 0,
            0, 1, 0, 0,
            0, 0, 1, 0,
            0, 0, 0, 1

        );

        return this;

    }

    clone(): Matrix4 {

        return new Matrix4().fromArray( this.elements );

    }

    copy( m: Matrix4 ): this {

        let te = this.elements;
        let me = m.elements;

        te[ 0 ] = me[ 0 ]; te[ 1 ] = me[ 1 ]; te[ 2 ] = me[ 2 ]; te[ 3 ] = me[ 3 ];
        te[ 4 ] = me[ 4 ]; te[ 5 ] = me[ 5 ]; te[ 6 ] = me[ 6 ]; te[ 7 ] = me[ 7 ];
        te[ 8 ] = me[ 8 ]; te[ 9 ] = me[ 9 ]; te[ 10 ] = me[ 10 ]; te[ 11 ] = me[ 11 ];
        te[ 12 ] = me[ 12 ]; te[ 13 ] = me[ 13 ]; te[ 14 ] = me[ 14 ]; te[ 15 ] = me[ 15 ];

        return this;

    }

    copyPosition( m: Matrix4 ): this {

        let te = this.elements, me = m.elements;

        te[ 12 ] = me[ 12 ];
        te[ 13 ] = me[ 13 ];
        te[ 14 ] = me[ 14 ];

        return this;

    }

    // extractBasis( xAxis: Vector3, yAxis: Vector3, zAxis: Vector3 ): this {
    //
    //     xAxis.setFromMatrixColumn( this, 0 );
    //     yAxis.setFromMatrixColumn( this, 1 );
    //     zAxis.setFromMatrixColumn( this, 2 );
    //
    //     return this;
    //
    // }

    makeBasis( xAxis: Vector3, yAxis: Vector3, zAxis: Vector3 ): this {

        this.set(
            xAxis.x, yAxis.x, zAxis.x, 0,
            xAxis.y, yAxis.y, zAxis.y, 0,
            xAxis.z, yAxis.z, zAxis.z, 0,
            0, 0, 0, 1
        );

        return this;

    }

    /**
     * Copies the rotation component of the supplied matrix m into this matrix rotation component.
     */
    // extractRotation( m: Matrix4 ): this {
    //
    //     // this method does not support reflection matrices
    //
    //     let te = this.elements;
    //     let me = m.elements;
    //
    //     let scaleX = 1 / _v1.setFromMatrixColumn( m, 0 ).length();
    //     let scaleY = 1 / _v1.setFromMatrixColumn( m, 1 ).length();
    //     let scaleZ = 1 / _v1.setFromMatrixColumn( m, 2 ).length();
    //
    //     te[ 0 ] = me[ 0 ] * scaleX;
    //     te[ 1 ] = me[ 1 ] * scaleX;
    //     te[ 2 ] = me[ 2 ] * scaleX;
    //     te[ 3 ] = 0;
    //
    //     te[ 4 ] = me[ 4 ] * scaleY;
    //     te[ 5 ] = me[ 5 ] * scaleY;
    //     te[ 6 ] = me[ 6 ] * scaleY;
    //     te[ 7 ] = 0;
    //
    //     te[ 8 ] = me[ 8 ] * scaleZ;
    //     te[ 9 ] = me[ 9 ] * scaleZ;
    //     te[ 10 ] = me[ 10 ] * scaleZ;
    //     te[ 11 ] = 0;
    //
    //     te[ 12 ] = 0;
    //     te[ 13 ] = 0;
    //     te[ 14 ] = 0;
    //     te[ 15 ] = 1;
    //
    //     return this;
    //
    // }

    // makeRotationFromEuler( euler: Euler ): this {
    //
    //     if ( ! ( euler && euler.isEuler ) ) {
    //
    //         console.error( 'THREE.Matrix4: .makeRotationFromEuler() now expects a Euler rotation rather than a Vector3 and order.' );
    //
    //     }
    //
    //     let te = this.elements;
    //
    //     let x = euler.x, y = euler.y, z = euler.z;
    //     let a = Math.cos( x ), b = Math.sin( x );
    //     let c = Math.cos( y ), d = Math.sin( y );
    //     let e = Math.cos( z ), f = Math.sin( z );
    //
    //     if ( euler.order === 'XYZ' ) {
    //
    //         let ae = a * e, af = a * f, be = b * e, bf = b * f;
    //
    //         te[ 0 ] = c * e;
    //         te[ 4 ] = - c * f;
    //         te[ 8 ] = d;
    //
    //         te[ 1 ] = af + be * d;
    //         te[ 5 ] = ae - bf * d;
    //         te[ 9 ] = - b * c;
    //
    //         te[ 2 ] = bf - ae * d;
    //         te[ 6 ] = be + af * d;
    //         te[ 10 ] = a * c;
    //
    //     } else if ( euler.order === 'YXZ' ) {
    //
    //         let ce = c * e, cf = c * f, de = d * e, df = d * f;
    //
    //         te[ 0 ] = ce + df * b;
    //         te[ 4 ] = de * b - cf;
    //         te[ 8 ] = a * d;
    //
    //         te[ 1 ] = a * f;
    //         te[ 5 ] = a * e;
    //         te[ 9 ] = - b;
    //
    //         te[ 2 ] = cf * b - de;
    //         te[ 6 ] = df + ce * b;
    //         te[ 10 ] = a * c;
    //
    //     } else if ( euler.order === 'ZXY' ) {
    //
    //         let ce = c * e, cf = c * f, de = d * e, df = d * f;
    //
    //         te[ 0 ] = ce - df * b;
    //         te[ 4 ] = - a * f;
    //         te[ 8 ] = de + cf * b;
    //
    //         te[ 1 ] = cf + de * b;
    //         te[ 5 ] = a * e;
    //         te[ 9 ] = df - ce * b;
    //
    //         te[ 2 ] = - a * d;
    //         te[ 6 ] = b;
    //         te[ 10 ] = a * c;
    //
    //     } else if ( euler.order === 'ZYX' ) {
    //
    //         let ae = a * e, af = a * f, be = b * e, bf = b * f;
    //
    //         te[ 0 ] = c * e;
    //         te[ 4 ] = be * d - af;
    //         te[ 8 ] = ae * d + bf;
    //
    //         te[ 1 ] = c * f;
    //         te[ 5 ] = bf * d + ae;
    //         te[ 9 ] = af * d - be;
    //
    //         te[ 2 ] = - d;
    //         te[ 6 ] = b * c;
    //         te[ 10 ] = a * c;
    //
    //     } else if ( euler.order === 'YZX' ) {
    //
    //         let ac = a * c, ad = a * d, bc = b * c, bd = b * d;
    //
    //         te[ 0 ] = c * e;
    //         te[ 4 ] = bd - ac * f;
    //         te[ 8 ] = bc * f + ad;
    //
    //         te[ 1 ] = f;
    //         te[ 5 ] = a * e;
    //         te[ 9 ] = - b * e;
    //
    //         te[ 2 ] = - d * e;
    //         te[ 6 ] = ad * f + bc;
    //         te[ 10 ] = ac - bd * f;
    //
    //     } else if ( euler.order === 'XZY' ) {
    //
    //         let ac = a * c, ad = a * d, bc = b * c, bd = b * d;
    //
    //         te[ 0 ] = c * e;
    //         te[ 4 ] = - f;
    //         te[ 8 ] = d * e;
    //
    //         te[ 1 ] = ac * f + bd;
    //         te[ 5 ] = a * e;
    //         te[ 9 ] = ad * f - bc;
    //
    //         te[ 2 ] = bc * f - ad;
    //         te[ 6 ] = b * e;
    //         te[ 10 ] = bd * f + ac;
    //
    //     }
    //
    //     // bottom row
    //     te[ 3 ] = 0;
    //     te[ 7 ] = 0;
    //     te[ 11 ] = 0;
    //
    //     // last column
    //     te[ 12 ] = 0;
    //     te[ 13 ] = 0;
    //     te[ 14 ] = 0;
    //     te[ 15 ] = 1;
    //
    //     return this;
    //
    // }

    // makeRotationFromQuaternion( q: Quaternion ): this {
    //
    //     return this.compose( _zero, q, _one );
    //
    // }

    /**
     * Constructs a rotation matrix, looking from eye towards center with defined up vector.
     */
    lookAt( eye: Vector3, target: Vector3, up: Vector3 ): this {

        let te = this.elements;

        _z.subVectors( eye, target );

        if ( _z.lengthSq() === 0 ) {

            // eye and target are in the same position

            _z.z = 1;

        }

        _z.normalize();
        _x.crossVectors( up, _z );

        if ( _x.lengthSq() === 0 ) {

            // up and z are parallel

            if ( Math.abs( up.z ) === 1 ) {

                _z.x += 0.0001;

            } else {

                _z.z += 0.0001;

            }

            _z.normalize();
            _x.crossVectors( up, _z );

        }

        _x.normalize();
        _y.crossVectors( _z, _x );

        te[ 0 ] = _x.x; te[ 4 ] = _y.x; te[ 8 ] = _z.x;
        te[ 1 ] = _x.y; te[ 5 ] = _y.y; te[ 9 ] = _z.y;
        te[ 2 ] = _x.z; te[ 6 ] = _y.z; te[ 10 ] = _z.z;

        return this;

    }

    /**
     * Multiplies this matrix by m.
     */
    multiply( m: Matrix4 ,n?:Matrix4): this {

        if ( n !== undefined ) {

            console.warn( 'THREE.Matrix4: .multiply() now only accepts one argument. Use .multiplyMatrices( a, b ) instead.' );
            return this.multiplyMatrices( m, n );

        }

        return this.multiplyMatrices( this, m );

    }

    premultiply( m: Matrix4 ): this {

        return this.multiplyMatrices( m, this );

    }

    /**
     * Sets this matrix to a x b.
     */
    multiplyMatrices( a: Matrix4, b: Matrix4 ): this {

        let ae = a.elements;
        let be = b.elements;
        let te = this.elements;

        let a11 = ae[ 0 ], a12 = ae[ 4 ], a13 = ae[ 8 ], a14 = ae[ 12 ];
        let a21 = ae[ 1 ], a22 = ae[ 5 ], a23 = ae[ 9 ], a24 = ae[ 13 ];
        let a31 = ae[ 2 ], a32 = ae[ 6 ], a33 = ae[ 10 ], a34 = ae[ 14 ];
        let a41 = ae[ 3 ], a42 = ae[ 7 ], a43 = ae[ 11 ], a44 = ae[ 15 ];

        let b11 = be[ 0 ], b12 = be[ 4 ], b13 = be[ 8 ], b14 = be[ 12 ];
        let b21 = be[ 1 ], b22 = be[ 5 ], b23 = be[ 9 ], b24 = be[ 13 ];
        let b31 = be[ 2 ], b32 = be[ 6 ], b33 = be[ 10 ], b34 = be[ 14 ];
        let b41 = be[ 3 ], b42 = be[ 7 ], b43 = be[ 11 ], b44 = be[ 15 ];

        te[ 0 ] = a11 * b11 + a12 * b21 + a13 * b31 + a14 * b41;
        te[ 4 ] = a11 * b12 + a12 * b22 + a13 * b32 + a14 * b42;
        te[ 8 ] = a11 * b13 + a12 * b23 + a13 * b33 + a14 * b43;
        te[ 12 ] = a11 * b14 + a12 * b24 + a13 * b34 + a14 * b44;

        te[ 1 ] = a21 * b11 + a22 * b21 + a23 * b31 + a24 * b41;
        te[ 5 ] = a21 * b12 + a22 * b22 + a23 * b32 + a24 * b42;
        te[ 9 ] = a21 * b13 + a22 * b23 + a23 * b33 + a24 * b43;
        te[ 13 ] = a21 * b14 + a22 * b24 + a23 * b34 + a24 * b44;

        te[ 2 ] = a31 * b11 + a32 * b21 + a33 * b31 + a34 * b41;
        te[ 6 ] = a31 * b12 + a32 * b22 + a33 * b32 + a34 * b42;
        te[ 10 ] = a31 * b13 + a32 * b23 + a33 * b33 + a34 * b43;
        te[ 14 ] = a31 * b14 + a32 * b24 + a33 * b34 + a34 * b44;

        te[ 3 ] = a41 * b11 + a42 * b21 + a43 * b31 + a44 * b41;
        te[ 7 ] = a41 * b12 + a42 * b22 + a43 * b32 + a44 * b42;
        te[ 11 ] = a41 * b13 + a42 * b23 + a43 * b33 + a44 * b43;
        te[ 15 ] = a41 * b14 + a42 * b24 + a43 * b34 + a44 * b44;

        return this;

    }

    /**
     * Multiplies this matrix by s.
     */
    multiplyScalar( s: number ): this {

        let te = this.elements;

        te[ 0 ] *= s; te[ 4 ] *= s; te[ 8 ] *= s; te[ 12 ] *= s;
        te[ 1 ] *= s; te[ 5 ] *= s; te[ 9 ] *= s; te[ 13 ] *= s;
        te[ 2 ] *= s; te[ 6 ] *= s; te[ 10 ] *= s; te[ 14 ] *= s;
        te[ 3 ] *= s; te[ 7 ] *= s; te[ 11 ] *= s; te[ 15 ] *= s;

        return this;

    }

    /**
     * Computes determinant of this matrix.
     * Based on http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm
     */
    determinant(): number {

        let te = this.elements;

        let n11 = te[ 0 ], n12 = te[ 4 ], n13 = te[ 8 ], n14 = te[ 12 ];
        let n21 = te[ 1 ], n22 = te[ 5 ], n23 = te[ 9 ], n24 = te[ 13 ];
        let n31 = te[ 2 ], n32 = te[ 6 ], n33 = te[ 10 ], n34 = te[ 14 ];
        let n41 = te[ 3 ], n42 = te[ 7 ], n43 = te[ 11 ], n44 = te[ 15 ];

        //TODO: make this more efficient
        //( based on http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm )

        return (
            n41 * (
                + n14 * n23 * n32
                - n13 * n24 * n32
                - n14 * n22 * n33
                + n12 * n24 * n33
                + n13 * n22 * n34
                - n12 * n23 * n34
            ) +
            n42 * (
                + n11 * n23 * n34
                - n11 * n24 * n33
                + n14 * n21 * n33
                - n13 * n21 * n34
                + n13 * n24 * n31
                - n14 * n23 * n31
            ) +
            n43 * (
                + n11 * n24 * n32
                - n11 * n22 * n34
                - n14 * n21 * n32
                + n12 * n21 * n34
                + n14 * n22 * n31
                - n12 * n24 * n31
            ) +
            n44 * (
                - n13 * n22 * n31
                - n11 * n23 * n32
                + n11 * n22 * n33
                + n13 * n21 * n32
                - n12 * n21 * n33
                + n12 * n23 * n31
            )

        );

    }

    /**
     * Transposes this matrix.
     */
    transpose(): this {

        let te = this.elements;
        let tmp;

        tmp = te[ 1 ]; te[ 1 ] = te[ 4 ]; te[ 4 ] = tmp;
        tmp = te[ 2 ]; te[ 2 ] = te[ 8 ]; te[ 8 ] = tmp;
        tmp = te[ 6 ]; te[ 6 ] = te[ 9 ]; te[ 9 ] = tmp;

        tmp = te[ 3 ]; te[ 3 ] = te[ 12 ]; te[ 12 ] = tmp;
        tmp = te[ 7 ]; te[ 7 ] = te[ 13 ]; te[ 13 ] = tmp;
        tmp = te[ 11 ]; te[ 11 ] = te[ 14 ]; te[ 14 ] = tmp;

        return this;

    }

    /**
     * Sets the position component for this matrix from vector v.
     */
    setPosition( x: number, y: number, z: number): this;
    setPosition( v: IVector3): this;
    setPosition( x: IVector3 | number, y?: number, z?: number ): this {

        let te = this.elements;

        if ( typeof x === 'number') {

            te[ 12 ] = x;
            te[ 13 ] = y!;
            te[ 14 ] = z!;

        }
        else {

            te[ 12 ] = x.x;
            te[ 13 ] = x.y;
            te[ 14 ] = x.z;

        }

        return this;

    }

    /**
     * Sets this matrix to the inverse of matrix m.
     * Based on http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm.
     */
    getInverse( m: Matrix4 ): this
    getInverse( m: Matrix4 ,throwOnDegenerate?: boolean ): this {

        if ( throwOnDegenerate !== undefined ) {

            console.warn( "THREE.Matrix4: .getInverse() can no longer be configured to throw on degenerate." );

        }

        // based on http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm
        let te = this.elements,
            me = m.elements,

            n11 = me[ 0 ], n21 = me[ 1 ], n31 = me[ 2 ], n41 = me[ 3 ],
            n12 = me[ 4 ], n22 = me[ 5 ], n32 = me[ 6 ], n42 = me[ 7 ],
            n13 = me[ 8 ], n23 = me[ 9 ], n33 = me[ 10 ], n43 = me[ 11 ],
            n14 = me[ 12 ], n24 = me[ 13 ], n34 = me[ 14 ], n44 = me[ 15 ],

            t11 = n23 * n34 * n42 - n24 * n33 * n42 + n24 * n32 * n43 - n22 * n34 * n43 - n23 * n32 * n44 + n22 * n33 * n44,
            t12 = n14 * n33 * n42 - n13 * n34 * n42 - n14 * n32 * n43 + n12 * n34 * n43 + n13 * n32 * n44 - n12 * n33 * n44,
            t13 = n13 * n24 * n42 - n14 * n23 * n42 + n14 * n22 * n43 - n12 * n24 * n43 - n13 * n22 * n44 + n12 * n23 * n44,
            t14 = n14 * n23 * n32 - n13 * n24 * n32 - n14 * n22 * n33 + n12 * n24 * n33 + n13 * n22 * n34 - n12 * n23 * n34;

        let det = n11 * t11 + n21 * t12 + n31 * t13 + n41 * t14;

        if ( det === 0 ) return this.set( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 );

        let detInv = 1 / det;

        te[ 0 ] = t11 * detInv;
        te[ 1 ] = ( n24 * n33 * n41 - n23 * n34 * n41 - n24 * n31 * n43 + n21 * n34 * n43 + n23 * n31 * n44 - n21 * n33 * n44 ) * detInv;
        te[ 2 ] = ( n22 * n34 * n41 - n24 * n32 * n41 + n24 * n31 * n42 - n21 * n34 * n42 - n22 * n31 * n44 + n21 * n32 * n44 ) * detInv;
        te[ 3 ] = ( n23 * n32 * n41 - n22 * n33 * n41 - n23 * n31 * n42 + n21 * n33 * n42 + n22 * n31 * n43 - n21 * n32 * n43 ) * detInv;

        te[ 4 ] = t12 * detInv;
        te[ 5 ] = ( n13 * n34 * n41 - n14 * n33 * n41 + n14 * n31 * n43 - n11 * n34 * n43 - n13 * n31 * n44 + n11 * n33 * n44 ) * detInv;
        te[ 6 ] = ( n14 * n32 * n41 - n12 * n34 * n41 - n14 * n31 * n42 + n11 * n34 * n42 + n12 * n31 * n44 - n11 * n32 * n44 ) * detInv;
        te[ 7 ] = ( n12 * n33 * n41 - n13 * n32 * n41 + n13 * n31 * n42 - n11 * n33 * n42 - n12 * n31 * n43 + n11 * n32 * n43 ) * detInv;

        te[ 8 ] = t13 * detInv;
        te[ 9 ] = ( n14 * n23 * n41 - n13 * n24 * n41 - n14 * n21 * n43 + n11 * n24 * n43 + n13 * n21 * n44 - n11 * n23 * n44 ) * detInv;
        te[ 10 ] = ( n12 * n24 * n41 - n14 * n22 * n41 + n14 * n21 * n42 - n11 * n24 * n42 - n12 * n21 * n44 + n11 * n22 * n44 ) * detInv;
        te[ 11 ] = ( n13 * n22 * n41 - n12 * n23 * n41 - n13 * n21 * n42 + n11 * n23 * n42 + n12 * n21 * n43 - n11 * n22 * n43 ) * detInv;

        te[ 12 ] = t14 * detInv;
        te[ 13 ] = ( n13 * n24 * n31 - n14 * n23 * n31 + n14 * n21 * n33 - n11 * n24 * n33 - n13 * n21 * n34 + n11 * n23 * n34 ) * detInv;
        te[ 14 ] = ( n14 * n22 * n31 - n12 * n24 * n31 - n14 * n21 * n32 + n11 * n24 * n32 + n12 * n21 * n34 - n11 * n22 * n34 ) * detInv;
        te[ 15 ] = ( n12 * n23 * n31 - n13 * n22 * n31 + n13 * n21 * n32 - n11 * n23 * n32 - n12 * n21 * n33 + n11 * n22 * n33 ) * detInv;

        return this;

    }

    /**
     * Multiplies the columns of this matrix by vector v.
     */
    scale( v: IVector3 ): this {

        let te = this.elements;
        let x = v.x, y = v.y, z = v.z;

        te[ 0 ] *= x; te[ 4 ] *= y; te[ 8 ] *= z;
        te[ 1 ] *= x; te[ 5 ] *= y; te[ 9 ] *= z;
        te[ 2 ] *= x; te[ 6 ] *= y; te[ 10 ] *= z;
        te[ 3 ] *= x; te[ 7 ] *= y; te[ 11 ] *= z;

        return this;

    }

    getMaxScaleOnAxis(): number {

        let te = this.elements;

        let scaleXSq = te[ 0 ] * te[ 0 ] + te[ 1 ] * te[ 1 ] + te[ 2 ] * te[ 2 ];
        let scaleYSq = te[ 4 ] * te[ 4 ] + te[ 5 ] * te[ 5 ] + te[ 6 ] * te[ 6 ];
        let scaleZSq = te[ 8 ] * te[ 8 ] + te[ 9 ] * te[ 9 ] + te[ 10 ] * te[ 10 ];

        return Math.sqrt( Math.max( scaleXSq, scaleYSq, scaleZSq ) );

    }

    /**
     * Sets this matrix as translation transform.
     */
    makeTranslation( x: number, y: number, z: number ): this {

        this.set(

            1, 0, 0, x,
            0, 1, 0, y,
            0, 0, 1, z,
            0, 0, 0, 1

        );

        return this;

    }

    /**
     * Sets this matrix as rotation transform around x axis by theta radians.
     *
     * @param theta Rotation angle in radians.
     */
    makeRotationX( theta: number ): this {

        let c = Math.cos( theta ), s = Math.sin( theta );

        this.set(

            1, 0, 0, 0,
            0, c, - s, 0,
            0, s, c, 0,
            0, 0, 0, 1

        );

        return this;

    }

    /**
     * Sets this matrix as rotation transform around y axis by theta radians.
     *
     * @param theta Rotation angle in radians.
     */
    makeRotationY( theta: number ): this {

        let c = Math.cos( theta ), s = Math.sin( theta );

        this.set(

            c, 0, s, 0,
            0, 1, 0, 0,
            - s, 0, c, 0,
            0, 0, 0, 1

        );

        return this;

    }

    /**
     * Sets this matrix as rotation transform around z axis by theta radians.
     *
     * @param theta Rotation angle in radians.
     */
    makeRotationZ( theta: number ): this {

        let c = Math.cos( theta ), s = Math.sin( theta );

        this.set(

            c, - s, 0, 0,
            s, c, 0, 0,
            0, 0, 1, 0,
            0, 0, 0, 1

        );

        return this;

    }

    /**
     * Sets this matrix as rotation transform around axis by angle radians.
     * Based on http://www.gamedev.net/reference/articles/article1199.asp.
     *
     * @param axis Rotation axis.
     * @param angle Rotation angle in radians.
     */
    makeRotationAxis( axis: IVector3, angle: number ): this {

        // Based on http://www.gamedev.net/reference/articles/article1199.asp

        let c = Math.cos( angle );
        let s = Math.sin( angle );
        let t = 1 - c;
        let x = axis.x, y = axis.y, z = axis.z;
        let tx = t * x, ty = t * y;

        this.set(

            tx * x + c, tx * y - s * z, tx * z + s * y, 0,
            tx * y + s * z, ty * y + c, ty * z - s * x, 0,
            tx * z - s * y, ty * z + s * x, t * z * z + c, 0,
            0, 0, 0, 1

        );

        return this;

    }

    /**
     * Sets this matrix as scale transform.
     */
    makeScale( x: number, y: number, z: number ): this {

        this.set(

            x, 0, 0, 0,
            0, y, 0, 0,
            0, 0, z, 0,
            0, 0, 0, 1

        );

        return this;

    }

    /**
     * Sets this matrix to the transformation composed of translation, rotation and scale.
     */
    // compose( position: VectorUp3, quaternion: Quaternion | Euler, scale: VectorUp3 ): this {
    //
    //     let te = this.elements;
    //
    //     // @ts-ignore
    //     let x = quaternion['_x'], y = quaternion['_y'], z = quaternion['_z'], w = quaternion['_w'];
    //     let x2 = x + x,	y2 = y + y, z2 = z + z;
    //     let xx = x * x2, xy = x * y2, xz = x * z2;
    //     let yy = y * y2, yz = y * z2, zz = z * z2;
    //     let wx = w * x2, wy = w * y2, wz = w * z2;
    //
    //     let sx = scale.x, sy = scale.y, sz = scale.z;
    //
    //     te[ 0 ] = ( 1 - ( yy + zz ) ) * sx;
    //     te[ 1 ] = ( xy + wz ) * sx;
    //     te[ 2 ] = ( xz - wy ) * sx;
    //     te[ 3 ] = 0;
    //
    //     te[ 4 ] = ( xy - wz ) * sy;
    //     te[ 5 ] = ( 1 - ( xx + zz ) ) * sy;
    //     te[ 6 ] = ( yz + wx ) * sy;
    //     te[ 7 ] = 0;
    //
    //     te[ 8 ] = ( xz + wy ) * sz;
    //     te[ 9 ] = ( yz - wx ) * sz;
    //     te[ 10 ] = ( 1 - ( xx + yy ) ) * sz;
    //     te[ 11 ] = 0;
    //
    //     te[ 12 ] = position.x;
    //     te[ 13 ] = position.y;
    //     te[ 14 ] = position.z;
    //     te[ 15 ] = 1;
    //
    //     return this;
    //
    // }

    /**
     * Decomposes this matrix into it's position, quaternion and scale components.
     */
    // decompose(
    //     position: IVector3,
    //     quaternion: Quaternion | Euler,
    //     scale: IVector3
    // ): this {
    //
    //     let te = this.elements;
    //
    //     let sx = _v1.set( te[ 0 ], te[ 1 ], te[ 2 ] ).length();
    //     let sy = _v1.set( te[ 4 ], te[ 5 ], te[ 6 ] ).length();
    //     let sz = _v1.set( te[ 8 ], te[ 9 ], te[ 10 ] ).length();
    //
    //     // if determine is negative, we need to invert one scale
    //     let det = this.determinant();
    //     if ( det < 0 ) sx = - sx;
    //
    //     position.x = te[ 12 ];
    //     position.y = te[ 13 ];
    //     position.z = te[ 14 ];
    //
    //     // scale the rotation part
    //     _m1.copy( this );
    //
    //     let invSX = 1 / sx;
    //     let invSY = 1 / sy;
    //     let invSZ = 1 / sz;
    //
    //     _m1.elements[ 0 ] *= invSX;
    //     _m1.elements[ 1 ] *= invSX;
    //     _m1.elements[ 2 ] *= invSX;
    //
    //     _m1.elements[ 4 ] *= invSY;
    //     _m1.elements[ 5 ] *= invSY;
    //     _m1.elements[ 6 ] *= invSY;
    //
    //     _m1.elements[ 8 ] *= invSZ;
    //     _m1.elements[ 9 ] *= invSZ;
    //     _m1.elements[ 10 ] *= invSZ;
    //
    //     quaternion.setFromRotationMatrix( _m1 );
    //
    //     scale.x = sx;
    //     scale.y = sy;
    //     scale.z = sz;
    //
    //     return this;
    //
    // }

    /**
     * Creates a frustum matrix.
     */
    makePerspective( left: number, right: number, top: number, bottom: number, near: number, far: number ): this {

        if ( far === undefined ) {

            console.warn( 'THREE.Matrix4: .makePerspective() has been redefined and has a new signature. Please check the docs.' );

        }

        let te = this.elements;
        let x = 2 * near / ( right - left );
        let y = 2 * near / ( top - bottom );

        let a = ( right + left ) / ( right - left );
        let b = ( top + bottom ) / ( top - bottom );
        let c = - ( far + near ) / ( far - near );
        let d = - 2 * far * near / ( far - near );

        te[ 0 ] = x;	te[ 4 ] = 0;	te[ 8 ] = a;	te[ 12 ] = 0;
        te[ 1 ] = 0;	te[ 5 ] = y;	te[ 9 ] = b;	te[ 13 ] = 0;
        te[ 2 ] = 0;	te[ 6 ] = 0;	te[ 10 ] = c;	te[ 14 ] = d;
        te[ 3 ] = 0;	te[ 7 ] = 0;	te[ 11 ] = - 1;	te[ 15 ] = 0;

        return this;

    }

    /**
     * Creates an orthographic projection matrix.
     */
    makeOrthographic( left: number, right: number, top: number, bottom: number, near: number, far: number ): this {

        let te = this.elements;
        let w = 1.0 / ( right - left );
        let h = 1.0 / ( top - bottom );
        let p = 1.0 / ( far - near );

        let x = ( right + left ) * w;
        let y = ( top + bottom ) * h;
        let z = ( far + near ) * p;

        te[ 0 ] = 2 * w;	te[ 4 ] = 0;	te[ 8 ] = 0;	te[ 12 ] = - x;
        te[ 1 ] = 0;	te[ 5 ] = 2 * h;	te[ 9 ] = 0;	te[ 13 ] = - y;
        te[ 2 ] = 0;	te[ 6 ] = 0;	te[ 10 ] = - 2 * p;	te[ 14 ] = - z;
        te[ 3 ] = 0;	te[ 7 ] = 0;	te[ 11 ] = 0;	te[ 15 ] = 1;

        return this;

    }

    equals( matrix: Matrix4 ): boolean {

        let te = this.elements;
        let me = matrix.elements;

        for ( let i = 0; i < 16; i ++ ) {

            if ( te[ i ] !== me[ i ] ) return false;

        }

        return true;

    }

    /**
     * Sets the values of this matrix from the provided array-like.
     * @param array the source array-like.
     * @param offset (optional) offset into the array-like. Default is 0.
     */
    fromArray( array: ArrayLike<number>, offset?: number ): Matrix4 {

        if ( offset === undefined ) offset = 0;

        for ( let i = 0; i < 16; i ++ ) {

            this.elements[ i ] = array[ i + offset ];

        }

        return this;

    }

    /**
     * Copies he values of this matrix into the provided array-like.
     * @param array array-like to store the matrix to.
     * @param offset (optional) optional offset into the array-like.
     * @return The provided array-like.
     */
    toArray(): number[];
    toArray( array?: number[], offset?: number ): number[] {

        if ( array === undefined ) array = [];
        if ( offset === undefined ) offset = 0;

        let te = this.elements;

        array[ offset ] = te[ 0 ];
        array[ offset + 1 ] = te[ 1 ];
        array[ offset + 2 ] = te[ 2 ];
        array[ offset + 3 ] = te[ 3 ];

        array[ offset + 4 ] = te[ 4 ];
        array[ offset + 5 ] = te[ 5 ];
        array[ offset + 6 ] = te[ 6 ];
        array[ offset + 7 ] = te[ 7 ];

        array[ offset + 8 ] = te[ 8 ];
        array[ offset + 9 ] = te[ 9 ];
        array[ offset + 10 ] = te[ 10 ];
        array[ offset + 11 ] = te[ 11 ];

        array[ offset + 12 ] = te[ 12 ];
        array[ offset + 13 ] = te[ 13 ];
        array[ offset + 14 ] = te[ 14 ];
        array[ offset + 15 ] = te[ 15 ];

        return array;

    }

}


const _v1 = new Vector3();
const _m1 = new Matrix4();
const _zero = new Vector3( 0, 0, 0 );
const _one = new Vector3( 1, 1, 1 );
const _x = new Vector3();
const _y = new Vector3();
const _z = new Vector3();
